Signs and fractions: authors' preferred method of reducing fractions is by multiplying the denominator by -1

[daledamos]

Hello, thank you in advance for any help.

I am working my way through Selby&Slavin's Practical Algebra self teaching guide.

In frame 17, 18 and 19 of chapter 5, Fractions, the authors explain their preferred method of reducing fractions by (1) multiplying the denominator by -1 and (2) then adjusting the signs for the numerator.

Can I simply find the same result by multiplying the whole fraction by negative 1? The authors method seems the unusually cumbersome but maybe I am missing something?

TY!!

 

[Harry_the_cat]

If you multiply the whole fraction by -1, you will change its value. So you can't do that.

BUT, you can multiply the whole fraction by \(\displaystyle \frac{-1}{-1}\), because this is equal to 1, so it won't change its value.

(I think that might have been what you wanted to do anyway??)

 

[daledamos]

YES! TY

 

[Dr.Peterson]

In frame 17, 18 and 19 of chapter 5, Fractions, the authors explain their preferred method of reducing fractions by (1) multiplying the denominator by -1 and (2) then adjusting the signs for the numerator.

Can I simply find the same result by multiplying the whole fraction by negative 1? The authors method seems the unusually cumbersome but maybe I am missing something?

There are many ways you can carry out the details equivalently. You (I think) want to multiply the numerator and denominator by -1. They want to multiply the denominator by -1 and multiply the entire fraction by -1 to compensate. My own preferred way is to factor out -1 from the bottom, and then move it outside. They all amount to the same thing. (Possibly if you showed us exactly what you would do, we might have additional suggestions for making it easier or safer.

When a textbook shows one method, never take it to mean that no other method works, or is as good.